ACold Inc is a frozen food distributor with 10 warehouses across the country, Ivan Tory, one...
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ACold Inc is a frozen food distributor with 10 warehouses across the country, Ivan Tory, one of the warehouse managers, wants to make sure that the inventory policies used by the warehouse are minimizing inventory while still maintaining quick delivery to ACold's customers. Since the warehouse carries hundreds of different products, Ivan decided to study one. He picked Caruso's Frozen Pizza (CFP). Average daily demand for CFPs is normally distributed with a mean of 395 and a standard deviation of 159. Since ACold orders at least one truck from their supplier each day, ACold can essentially order any quantity of CFP it wants each day. In fact, ACold's computer system is designed to implement an order-up-to policy for each product. Ivan notes that any order for CFPs arrives 3 days after the order. Suppose an order-up-to level of 2458 is used. What is the expected on-hand inventory? Use Table 14.1 and round to nearest integer. Suppose an order-up-to level of 2439 is used. What is the expected on-order inventory? Round your answer to the nearest integer. Suppose an order-up-to level of 2032 is used. What is the in-stock probability? Use Table 14.1. Round your answer to one decimal. d. Suppose ACold wants a 0.92 in-stock probability. What should the order-up-to level be? Use Table 14.1 Round your answer to the nearest integer 10 TABLE 14.1 The Distribution Function, Fj, and the Inventory Function, f), for the Standard Normal Distribution Function (2) 2 -4.0 -3.9 <-3.8 -3.7 -3.6 -35 -3.4 -3.3 -3.2 -3.1 -3.0 -29 -28 -2.7 -2.5 -2.4 -2.3 -2.2 -2.1 -2.0 -1.9 -1.8 -1.7 -1.6 <-15 <-14 -1.3 -12 -1.1 -1.0 -0.9 0.8 -0.7 -0.6 <-05 -04 <-03 -02 -0.1 0.0 F(2) 0000 0000 0001 0001 0002 0002 0003 0005 0007 0010 0013 0019 0026 0035 0047 0062 0082 0107 0139 0179 0228 0287 0359 0446 0548 0668 0808 0968 1151 1357 1587 1841 2119 2420 2743 3085 3446 3821 4207 5000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0001 0.0001 0.0002 0.0003 0.0004 0.0005 0.0008 0.0011 0.0015 0.0020 0.0027 0.0037 0.0049 0.0065 0.0085 00111 0.0143 0.0183 0.0232 00293 0.0367 0.0455 0.0561 0.0686 0.0833 0.1004 01202 0.1429 0.1607 0 1978 0.2304 02668 03069 0,3509 2 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 22 2.3 2.5 232323223333228 2.6 2.7 2.9 30 31 3.4 3.5 35 37 39 40 Fp) 5398 5793 6179 5554 6915 7257 7580 7881 8159 8413 8643 8849 9032 9192 9332 9452 9554 9641 9713 9772 9921 9661 9893 9918 9938 9953 9965 9974 0981 9982 9990 9993 9995 9997 9998 9998 9900 10000 (2) 0.4509 0.5069 0.5668 0.6304 0.6978 0.7687 0.8429 0.9202 1.0004 1.0833 1.1686 1.2561 1.3455 1.4367 1.5293 1.6232 1.7183 1.8143 19111 2.0065 2.1065 22049 2:3037 2.4027 2.5020 2.0015 27011 2.8008 29005 3.0004 31003 3.2002 3,3001 3.4001 3.5001 16000 3.7000 1.8000 39000 ACold Inc is a frozen food distributor with 10 warehouses across the country, Ivan Tory, one of the warehouse managers, wants to make sure that the inventory policies used by the warehouse are minimizing inventory while still maintaining quick delivery to ACold's customers. Since the warehouse carries hundreds of different products, Ivan decided to study one. He picked Caruso's Frozen Pizza (CFP). Average daily demand for CFPs is normally distributed with a mean of 395 and a standard deviation of 159. Since ACold orders at least one truck from their supplier each day, ACold can essentially order any quantity of CFP it wants each day. In fact, ACold's computer system is designed to implement an order-up-to policy for each product. Ivan notes that any order for CFPs arrives 3 days after the order. Suppose an order-up-to level of 2458 is used. What is the expected on-hand inventory? Use Table 14.1 and round to nearest integer. Suppose an order-up-to level of 2439 is used. What is the expected on-order inventory? Round your answer to the nearest integer. Suppose an order-up-to level of 2032 is used. What is the in-stock probability? Use Table 14.1. Round your answer to one decimal. d. Suppose ACold wants a 0.92 in-stock probability. What should the order-up-to level be? Use Table 14.1 Round your answer to the nearest integer 10 TABLE 14.1 The Distribution Function, Fj, and the Inventory Function, f), for the Standard Normal Distribution Function (2) 2 -4.0 -3.9 <-3.8 -3.7 -3.6 -35 -3.4 -3.3 -3.2 -3.1 -3.0 -29 -28 -2.7 -2.5 -2.4 -2.3 -2.2 -2.1 -2.0 -1.9 -1.8 -1.7 -1.6 <-15 <-14 -1.3 -12 -1.1 -1.0 -0.9 0.8 -0.7 -0.6 <-05 -04 <-03 -02 -0.1 0.0 F(2) 0000 0000 0001 0001 0002 0002 0003 0005 0007 0010 0013 0019 0026 0035 0047 0062 0082 0107 0139 0179 0228 0287 0359 0446 0548 0668 0808 0968 1151 1357 1587 1841 2119 2420 2743 3085 3446 3821 4207 5000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0001 0.0001 0.0002 0.0003 0.0004 0.0005 0.0008 0.0011 0.0015 0.0020 0.0027 0.0037 0.0049 0.0065 0.0085 00111 0.0143 0.0183 0.0232 00293 0.0367 0.0455 0.0561 0.0686 0.0833 0.1004 01202 0.1429 0.1607 0 1978 0.2304 02668 03069 0,3509 2 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 22 2.3 2.5 232323223333228 2.6 2.7 2.9 30 31 3.4 3.5 35 37 39 40 Fp) 5398 5793 6179 5554 6915 7257 7580 7881 8159 8413 8643 8849 9032 9192 9332 9452 9554 9641 9713 9772 9921 9661 9893 9918 9938 9953 9965 9974 0981 9982 9990 9993 9995 9997 9998 9998 9900 10000 (2) 0.4509 0.5069 0.5668 0.6304 0.6978 0.7687 0.8429 0.9202 1.0004 1.0833 1.1686 1.2561 1.3455 1.4367 1.5293 1.6232 1.7183 1.8143 19111 2.0065 2.1065 22049 2:3037 2.4027 2.5020 2.0015 27011 2.8008 29005 3.0004 31003 3.2002 3,3001 3.4001 3.5001 16000 3.7000 1.8000 39000
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Matching Supply with Demand An Introduction to Operations Management
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3rd edition
Authors: Gerard Cachon, Christian Terwiesch
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